Question

tyler believes that an 8 - sided die can be used to predict whether customers at his store will use a coupon when making their purchases, with a roll of 1 indicating a coupon and all other outcomes indicating no coupon. today, 4 of the first 48 customers in the store used a coupon. how does the experimental probability of a customer using a coupon compare to the theoretical probability of tylers die? the experimental probability is greater than the theoretical probability by more than 2%. the experimental probability is less than the theoretical probability by more than 2%. the experimental probability is greater than the theoretical probability, but within 2%. the experimental probability is less than the theoretical probability, but within 2%.

Explanation:

Step1: Calculate theoretical probability

A fair 8 - sided die has 8 possible outcomes. The probability of rolling a 1 (indicating a coupon) is $P_{theoretical}=\frac{1}{8}=0.125 = 12.5\%$.

Step2: Calculate experimental probability

4 out of 48 customers used a coupon. So $P_{experimental}=\frac{4}{48}=\frac{1}{12}\approx0.0833 = 8.33\%$.

Step3: Find the difference

The difference between the theoretical and experimental probabilities is $12.5\%-8.33\% = 4.17\%$. Since $P_{experimental}

Answer:

The experimental probability is less than the theoretical probability by more than 2%.